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Within the framework of the Einstein's standard equations of the generaltheory of relativity, flat galactic rotational curves of galaxies cannot beexplained without hypothesis attracting the dark matter, the particles of whichhad not yet been identified. The vacuum central-symmetric solution of theequations of conformal gravitation is well known as metrics ofMannheim-Kazanas, on the basis of which these curves receive purely geometricalexplanation. We show in our work that the metrics of Mannheim-Kazanas is thesolution of not only Bach equations received from conformal-invariant WeylLagrangian, but also the solution of equations of the conformalgeometrodynamics at a nonzero vector of Weyl. In this connection the hypothesisis formulated that the space on galactic scales can be described not only byRiemannian geometry, but with geometry of Weyl.

The Mannheim-Kazanas solution, the conformal geometrodynamics and the dark matter